where \(\mathbf {e} \in \mathbb {R}^{n}\)  is the vector of ones and \(\otimes \)  denotes the Hadamard product of two vectors.
To avoid solving the above binary optimization problem, Zhao [1]} suggests solving the tightest convex relaxation of (REF ) instead.
That is, replacing the binary constraint by its convex hull, we obtain the following convex relaxation of the problem (REF ):
\(\overline{w}=\arg \min _{w}\left\lbrace f(u \otimes w): ~ \mathbf {e}^{T} w=k, ~ 0 \le w \le \mathbf {e} \right\rbrace .\) 
